Baryon susceptibilities, nongaussian moments and the QCD critical point

We calculate model-independently the impact of the critical point on higher order baryon susceptibilities $\chi_n$, showing how they depend on fluctuations of the order parameter. Including all tree level diagrams, we find new contributions to $\chi_4$ equally important to the kurtosis of the order parameter fluctuations, and we characterize the kurtosis and other nonguassian moments as functions on the phase diagram. Important features of this analysis are then confirmed by a Gross-Neveu model study with good agreement with other model studies as well as lattice and experimental data. This suggests the universality of the characteristic peak in baryon susceptibilities as a signal of the critical point. We discuss leveraging measurements of different $\chi_n$ to extrapolate the location of the critical point.